Solution for spherical cavity expansion in state-dependent soils

This work presents a spherical cavity expansion solution aimed at linking soil constitutive behavior with quantities that bear direct engineering meanings for practicing engineers (e.g., foundation bearing capacity). For this purpose, we derive the solution based on the state-dependent, critical state constitutive model proposed by Li and Dafalias (Geotechnique 50(4): 449–460, 2000), whose ability to realistically represent the actual mechanical behavior of sand has been extensively verified in the literature. To ensure the reliability of the solution, we verify it against an independent finite element analysis of spherical cavity expansion in solid governed by the same constitutive model. In this validation, we also highlight the dependence of cavity expansion response on the current state of granular materials relative to critical state. The application of the proposed solution in solving engineering problems is demonstrated in predicting the resistance of cone penetration and the ground movements associated with static pipe bursting in sand. We show that, based on the soil parameters determined from laboratory triaxial tests, the proposed solution can reasonably represent the dependence of cone penetration resistance on the density and pressure level of sand, as revealed from centrifuge testing. By comparing with finite element analysis, we demonstrate that the proposed solution can provide useful estimations for soil displacements caused by pipe bursting operation. These archetypal examples suggest that the proposed cavity expansion solution can form a theoretical basis for linking fundamental soil properties with quantities that have direct implications for geotechnical engineering practice.